Simplify the following expression: $ k = \dfrac{-9y - 6}{10y + 9} + \dfrac{-5}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-9y - 6}{10y + 9} \times \dfrac{7}{7} = \dfrac{-63y - 42}{70y + 63} $ Multiply the second expression by $\dfrac{10y + 9}{10y + 9}$ $ \dfrac{-5}{7} \times \dfrac{10y + 9}{10y + 9} = \dfrac{-50y - 45}{70y + 63} $ Therefore $ k = \dfrac{-63y - 42}{70y + 63} + \dfrac{-50y - 45}{70y + 63} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{-63y - 42 - 50y - 45}{70y + 63} $ $k = \dfrac{-113y - 87}{70y + 63}$